Oscillatory Sweep Measurements

In this case, the strain amplitude is kept constant in the linear viscoelastic region (usually, a point is taken far from y but not too low - that is in the midpoint of the linear viscoelastic region) and measurements are carried out as a function of frequency. Both, G and G are increased with an increase in frequency and ultimately, above a certain frequency, they reach a Hmiting value and show little dependence on frequency. G is higher than G in the low-frequency regime it also increases with increase in frequency and at a certain characteristic frequency 00 (which depends on the system) it becomes equal to G (this is usually referred to as the cross-over point), after which it reaches a maximum and then shows a reduction with further increase in frequency. 

The relaxation time may be used as a guide for the state of the dispersion. For a colloidally stable dispersion (at a given particle size distribution), r increases with increase of the volume fraction of the disperse phase, / . In other words, the cross-over point shifts to lower frequency with increase in / . For a given dispersion, r increases with increase in flocculation, provided that the particle size distribution remains the same (i.e., no Ostwald ripening). 

The value of G also increases with increase in flocculation, since aggregation of the particles usually results in liquid entrapment and the effective volume fraction of the dispersion will show an apparent increase. With flocculation, the net attraction between the particles also increases, and this results in an increase in G. The latter is determined by the number of contacts between the particles and the strength of each contact (which is determined by the attractive energy). 

It should be mentioned that, in practice, the full curve may not be obtained due to the frequency limit of the instrument, and also that measurements at low frequency are time-consuming. In fact, only part of the frequency dependence of G and G is usually obtained, and in most cases the system will be more elastic than viscous. 

Most disperse systems used in practice are weakly flocculated, and they also contain thickeners or structuring agents to reduce sedimentation and to acquire the correct rheological characteristics for applications, such as handcreams and lotions. The exact values of G and G required will depend on the system 

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An alternative rheological technique for assessing flocculation involves oscillatory measurements which, as noted above, can include two sets of experiments, namely strain and oscillatory sweep measurements. 

In oscillatory measurements, two sets of experiments are carried out, namely strain sweep measurements and oscillatory sweep measurement. 

In oscillatory measurements one carries out two sets of experiments, strain sweep and oscillatory sweep, which are detailed below. 

In oscillatory measurements one carries out two sets of experiments (i) Strain sweep measurements. In this case, the oscillation is fixed (say at 1 Hz) and the viscoelastic parameters are measured as a function of strain amplitude. This allows one to obtain the linear viscoelastic region. In this region all moduli are independent of the appUed strain amplitude and become only a function of time or frequency. This is illustrated in Fig. 3.50, which shows a schematic representation of the variation of G, G and G" with strain amplitude (at a fixed frequency). It can be seen from Fig. 3.49 that G, G and G" remain virtually constant up to a critical strain value, y . This region is the linear viscoelastic region. Above y, G and G start to fall, whereas G" starts to increase. This is the nonlinear region. The value of y may be identified with the minimum strain above which the "structure of the suspension starts to break down (for example breakdown of floes into smaller units and/or breakdown of a structuring agent). 

In the oscillatory sweep experiment, the strain amplitude is kept constant in the linear viscoelastic region (one usually takes a point far from y, but not too low, i.e. in the midpoint of the linear viscoelastic region) and measurements are carried out as a function of frequency. This is schematically represented in Fig. 3.50 for a viscoelastic liquid system. 

The evolution of the dynamic viscosity rp (co, x) or of the dynamic shear complex modulus G (co.x) as a function of conversion, x, can be followed by dynamic mechanical measurements using oscillatory shear deformation between two parallel plates at constant angular frequency, co = 2irf (f = frequency in Hz). In addition, the frequency sweep at certain time intervals during a slow reaction (x constant) allows determination of the frequency dependence of elastic quantities at the particular conversion. During such experiments, storage G (co), and loss G"(co) shear moduli and their ratio, the loss factor tan8(co), are obtained ... 

The four variables in dynamic oscillatory tests are strain amplitude (or stress amplitude in the case of controlled stress dynamic rheometers), frequency, temperature and time (Gunasekaran and Ak, 2002). Dynamic oscillatory tests can thus take the form of a strain (or stress) amplitude sweep (frequency and temperature held constant), a frequency sweep (strain or stress amplitude and temperature held constant), a temperature sweep (strain or stress amplitude and frequency held constant), or a time sweep (strain or stress amplitude, temperature and frequency held constant). A strain or stress amplitude sweep is normally carried out first to determine the limit of linear viscoelastic behavior. In processing data from both static and dynamic tests it is always necessary to check that measurements were made in the linear region. This is done by calculating viscoelastic properties from the experimental data and determining whether or not they are independent of the magnitude of applied stresses and strains. 

Rheology. The rheological properties of the blends and their components were determined on a Rheometrics Mechanical Spectrometer (RMS 800). Three kinds of dynamic oscillatory measurements (i.e. temperature, time, and frequency sweeps) were carried out. All experiments were done by using a parallel plate attachment with a radius of 12.5 mm and a gap setting from 1.2 to 1.8 mm. There was no significant dependence of the experimental results on the gap setting. 

For most oscillatory measurements, one has to control multiple variables, ramp (cover a range of values with a set rate of change) one variable, and measure several more variables. Classical oscillatory measurements included on most systems are stress sweeps, frequency sweeps, time sweeps, and temperature sweeps (if a pettier unit is included). 

Dynamic mechanical properties are measured to evaluate melt rheology of thermoplastics with and without additives which may modify rheological characteristics of these compositions. " Dynamic oscillatory shear rheometers are used for these purposes. Two geometries of test fixtures are used including parallel plates and cone and plate. Instrument use for these measurements must be capable of measuring forces (stress or strain) and frequency. Temperature must be controlled in a broad range and various modes of temperature sweeps should be available. Sample geometry is not specified but it should be suitable for measurement in particular experimental setup. 

Measurement modes oscillatory TMA-mode creep/relaxation (optional), stress/strain sweep (optional)... 

The linear viscoelastic response of LDPE/LDH nanocomposites has been studied using dynamic oscillatory measurements at constant strain amplitude of 2% and frequency sweep of 0.05-100 rad s . The response of aU nanocomposites is found to be quahtatively similar in the temperature range 160-240 °C. However, the time-temperature superposition principle is not... 

Dynamic viscoelastic parameters such as the storage modulus and the loss modulus offer another measure of the mechanical properties of hydrogels. The storage and loss moduli represent the stored energy (elastic portion) and the heat dissipated (viscous portion) respectively of a viscoelastic solid. These are determined using a rheometer. The most commonly used set up for these measurements is the rotational rheometer wherein the sample is placed between two discs, the top disc rotates in an oscillatory manner in order to introduce a small strain oscillatory shear, while the torque exerted by the sample on the lower disc is measured. This allows a shear stress-strain relationship to be determined and thus for the moduli in turn to be found. Usually an amplitude sweep will be done to ensure that the sample is in the linear viscoelastic range [73, 75, 79, 80]. 

Amplitude sweeps are oscillatory tests performed at variable amplitudes, keeping the frequency and also the measuring temperature constant. A typical frequency value used is 10 rad/s. Nonetheless, it is important to stress that some samples show a remarkable frequency dependence. There are two possibilities either a strain sweep or a stress sweep. At low amplitude values, in the so-called linear viscoelastic region, both storage and loss moduli show a constant plateau. 

The oscillatory measurements were carried out to investigate visco-elastic properties of binary HPMC/SDS mixtures, as well as of the separated coacervate phase in ternary HPMC/NaCMC/SDS systems. The amplitude sweep method was used. The oscillating frequency was 1 Hz. Plateau values of elastic, G , and viscous modulus, G , were determined from the linear visco-elastic region with the confidence band of 95%. Relative contribution of viscous to elastic component of the investigated structured systems was evaluated by means of the tanS value ... 

Dynamic mechanical relaxation was measured with a Perkin Elmer model 7e DMA working in the bending mode with an oscillatory strain. The complex modulus, E = E + iE , of each sample was determined over a temperature range from 173 to 423 K at a constant frequency of 1 Hz. Dielectric measurements in the temperature range from -223 to 403 K at a constant fi equency of 100 Hz were performed using a DEA 2970 high-performance dielectric spectrometer of TA Instruments. Temperature sweeps were performed at constant frequency with thermal stability better than 0.2 K. Measurements were performed under nitrogen atmosphere to avoid water absorption. 

An oscillatory rheometer (RMS 800) was used with a plate-plate fixture at 250 °C. Dynamic moduli and complex viscosity were measured by a frequency sweep from 0.1 to 100 rad/s. All samples used for the measurements were prepared with the same thermal history. In the case of the modified samples, a time sweep at a constant frequency (10 rad/sec) was carried out to confirm the absence of unreacted modifier in the sample before each frequency sweep. 

An Advanced Rheometric Expansion System (ARES, TA Instruments) was used in oscillatory shear mode with parallel plate geometry. Strain amplitude was fixed at 2% and dynamic frequency sweep experiments with angular frequency ( ) from 0.1 to 100 s were performed at 280°C. PET and all blends were tested under nitrogen atmosphere, while pure LCP, which was found not to degrade, was tested under air. The complex viscosity ( 7 ), dynamic storage (GO and loss (G") moduli were obtained. All rheological measurements are an average of four runs. 

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